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Combinatoria Enumerativa: Factorial, Grupo Simetrico, Ejemplos de Funciones Generadoras, Coeficiente Binomial, Funcion Generadora

Combinatoria Enumerativa: Factorial, Grupo Simetrico, Ejemplos de Funciones Generadoras, Coeficiente Binomial, Funcion Generadora


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About the Book

Fuente: Wikipedia. Paginas: 33. Capitulos: Factorial, Grupo simetrico, Ejemplos de funciones generadoras, Coeficiente binomial, Funcion generadora, Funcion W de Lambert, Numero de Dedekind, Factoradico, Problema de Flavio Josefo, Combinadico, Principio de inclusion-exclusion, Principio del palomar, Numeros de Catalan, Lema fundamental de teoria de cribas, Transformada binomial, Principio de la suma, Secuencia de Prufer, Tabla de Young, Problema de Catalan, Combinatoria, Subfactorial, Identidades de Newton, Formula de Stirling, Meandro, Numeros de Delannoy, Numero de Bell, Regla del producto, Regla de Golomb, Matroide, Anticadena, Permutacion circular. Extracto: Los siguientes ejemplos de funciones generadoras se presentan siguiendo el espiritu de George Polya, que abogaba por el aprendizaje de las matematicas haciendo y repasando tantos ejemplos y pruebas como fuese posible. El objetivo de este articulo es presentar trucos comunes del oficio en su contexto, de manera que el lector pueda incorporarlos a sus conocimientos. Se pueden crear nuevas funciones generadoras expandiendo otras funciones generadoras mas simples. Por ejemplo, comenzando con: y sustituyendo por, obtenemos: Consideremos el problema de hallar una formula cerrada para los numeros de Fibonacci Fn definidos por F0 = 0, F1 = 1, y Fn = Fn 1 + Fn 2 para n 2. Formamos la funcion generadora ordinaria para esta sucesion. La funcion generadora para la sucesion (Fn 1) es xf y la de (Fn 2) es xf. A partir de la relacion de recurrencia, vemos, por lo tanto, que la serie de potencias xf + xf concuerda con f excepto en los dos primeros coeficientes: Teniendo en cuenta estos, hallamos que (Este es el paso crucial; las relaciones recurrentes casi siempre pueden traducirse a ecuaciones para las funciones generadoras.) Resolviendo esta ecuacion para f, obtenemos El denominador puede factorizarse utilizando la proporcion aurea 1 = (1 + 5)/2 y 2 = (1 5)/2, y la tecnica de descomposicion en fracciones parci...


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Product Details
  • ISBN-13: 9781232477563
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 34
  • Spine Width: 2 mm
  • Weight: 82 gr
  • ISBN-10: 1232477567
  • Publisher Date: 27 May 2011
  • Binding: Paperback
  • Language: Spanish
  • Returnable: N
  • Sub Title: Factorial, Grupo Simetrico, Ejemplos de Funciones Generadoras, Coeficiente Binomial, Funcion Generadora
  • Width: 189 mm


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